Recall that `sinx + cosx =u` (say)
and `sin x cosx =v` (say) are connected by
`(sinx +cosx)^(2) = sin^(2)x + cos^(2)x+2sin cosx`
`rArr u^(2) = 1+2v`
`rArr v=(u^(2)-1)/(2)`
It follows that any rational integral function of `sinx + cosx`, and `sinx cosx` i.e., `R(sinx + cosx, sinx cosx)`, or in our notation R(u,v) can be transformed to `R(u, (u^(2)-1)/2)`. Thus, to solve an equation of the form `R(u,v)=0`, we form a polynomial equation in u and than look for solutions.
The number of solutions of the equation `sin theta + costheta=1 + sintheta costheta` in the interval `[0,4pi]` is

Options

A. Four
B. Six
C. Eight
D. Five

Answer

A